Statement 1: If the system of equations $x + k y + 3 z = 0, 3 x + k y - 2 z = 0, 2 x + 3 y - 4 z = 0$ has a nontrivial solution, then the value of $k$ is $\frac { 31 } { 2 }$. Statement 2: A system of three homogeneous equations in three variables has a non trivial solution if the determinant of the coefficient matrix is zero. (1) Statement 1 is false, Statement 2 is true. (2) Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1. (3) Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1. (4) Statement 1 is true, Statement 2 is false.
Statement 1: If the system of equations $x + k y + 3 z = 0, 3 x + k y - 2 z = 0, 2 x + 3 y - 4 z = 0$ has a nontrivial solution, then the value of $k$ is $\frac { 31 } { 2 }$.\\
Statement 2: A system of three homogeneous equations in three variables has a non trivial solution if the determinant of the coefficient matrix is zero.\\
(1) Statement 1 is false, Statement 2 is true.\\
(2) Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1.\\
(3) Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1.\\
(4) Statement 1 is true, Statement 2 is false.